Correcting one error in channels with feedback

TL;DR

This paper develops optimal transmission strategies for correcting a single error in discrete channels with feedback, showing that minimal feedback can achieve the same capacity as full feedback in binary channels.

Contribution

It introduces a method for constructing optimal strategies with limited feedback and demonstrates that two feedbacks suffice for binary channels to match complete feedback performance.

Findings

Two feedbacks are sufficient for binary channels to achieve full feedback capacity.

Constructed strategies for small lengths in binary asymmetric channels.

Proved that one error correction with feedback can be optimally managed.

Abstract

We address the problem of correcting a single error in an arbitrary discrete memoryless channel with error-free instantaneous feedback. For the case of a one-time feedback, we propose a method for constructing optimal transmission strategies. The obtained result allows us to prove that for a binary channel, two feedbacks are sufficient to transmit the same number of messages as in the case of complete feedback. We also apply the developed techniques to a binary asymmetric channel to construct transmission strategies for small lengths.